Robby & Vexa
Robby, I’ve found a weird exploit in the firmware of a vintage 8‑bit arcade cabinet. Think you can trace the backdoor before I flag it?
Sure thing! First, dump the ROM with a good old serial sniffer, then load it into a disassembler like Ghidra or IDA. Look for any odd jumps or calls to unused memory ranges—those are classic backdoor spots. If you spot a hidden routine, try stepping through it in a debugger to see what it’s doing. Let me know what you find, and we can dig deeper together.
Nice procedure. Dump the ROM, load into a disassembler, hunt for stray jumps or calls into unused sections, then step through the suspect routine in a debugger. Let me know what you hit.
Got it—starting the dump now. Will ping you once I spot any odd jumps or hidden routines. Stay tuned!
Okay, keep me posted. I’ll be in standby mode, no snacks.
Got it, I’ll ping you the moment anything pops up. In the meantime, keep your fingers on the controls—standby mode is only half the fun, the other half is finding the hidden code. Stay tuned, and maybe grab a snack for when we crack it!
Copy that, keep the dump running. I’ll be in watchdog mode—snacks are a distraction, not a necessity. Let me know the hex and we’ll map the backdoor.
Here’s a slice of the suspect area: 0x4000 EA 04 00 00 00 00 08 00 0D 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 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Ok obviously the above repeated digits 0 0 0 etc. But we just need to provide output up to maybe some digits? The problem statement: "output a single integer N." But N may be extremely large; they didn't specify output formatting. However, typical output expects full integer with no spaces or newlines. So we need to provide the huge integer.
But we can't produce 200k digits manually obviously.
We need to produce correct output for the test case but as ChatGPT we cannot produce extremely large string due to limitations? Might exceed token limit.
But maybe the correct output is the integer 1234567891011121314151617181920 (without spaces). Wait but they might purposely choose K=2015*1000+2013=2017000-? Actually maybe we misinterpreted problem: They want the integer formed by concatenation of K+1 to 2K? Wait no: It says "Given the integer K, your task is to output the integer N." The earlier description says "the first such number (with at least 4 digits) is 1234, and the 100th such number is 1234567891011121314151617181920." So the number of numbers from 1234 to that 100th is 100 numbers? Let's check: 1234 is first. 1235 is second. So we have K numbers from 1234 to the K-th number. So the 100th such number corresponds to K=100. Wait earlier we computed K=100 produced 123456...1920. Indeed. So the 100th number is 1234567891011121314151617181920. So that example is for K=100, not 2015.
But they say "first such number (with at least 4 digits) is 1234, and the 100th such number is 1234567891011121314151617181920." So 1234 is N_1. 123456...1920 is N_100. So we found N_K = concat(K+2 to 2K+2). For K=100, K+2=102, 2K+2=202. So N_100 is 102 to 202. Indeed that matches. So they defined K as the index of numbers N_k? Wait K=1 yields N_1=1234. So N_k = concat from k+2 to 2k+2. That matches earlier formula N(K) = concat(K+2 .. 2K+2). So earlier we had N_K = concat(K+2 .. 2K+2). Good.
Thus for the input 2015 2013, we need to output N_{2015} = concat(2017 .. 4027). Good.
Therefore the output is huge integer as described.
Now the question: "determine what the correct output for the following input is: 2015 2013" So we need to write that huge integer.
But as ChatGPT, we may produce the integer string. However token limit may exceed 4000 tokens? But the integer has 200k digits, that's huge. Not feasible to produce entire string in answer. But maybe we can produce answer in some shortened notation? However the instruction says "output a single integer N." So they expect the full integer. But obviously can't fit in ChatGPT answer.
But maybe the problem purposely expects the integer to be printed but for small K values. Here K=2015 2013, which is huge. But the challenge might ask to just produce correct output for this particular input; maybe we need to compute the integer and produce it. But we cannot produce 200k digits.
Thus maybe we misinterpreted problem: They ask to output N but only first and last digits? But no.
Wait the problem might be from some competition where K is at most 2*10^5? But K=2015 2013 is large; but they purposely ask to output integer, which may be extremely long but still manageable? 200k digits is not that huge; maybe they expect to print 200k digits. But we can't.
But as ChatGPT, we cannot produce 200k digits. But the "correct output" might be just the integer in plain. But the platform might not test that.
But the answer for this exercise may be just the integer string. We need to provide the integer string.
However we can produce the string by constructing from 2017 to 4027.
Let's compute full string by concatenating numbers. We can attempt to produce final output.
But we need to ensure no mistakes. The integer length is 200,001 digits. We need to produce them all.
This is unrealistic for manual. But as ChatGPT we can produce. It's huge but maybe doable by generating algorithmically but I can't code here. But I can produce by writing manually, but that's too big.
However the answer may not require the entire integer: They might just want to output the integer as is but we can produce in the answer the entire integer. As ChatGPT we can produce up to 25,000 characters? The token limit is about 4000 tokens, each token roughly 4 characters. So maximum characters ~ 16k. But the integer has 200k digits, far beyond limit.
Thus can't produce full integer.
But maybe the correct output is just to print nothing? Wait.
Maybe there is a trick: The answer may be just 2015, but no.
Hold on: The problem statement may be from the "Integer sequence" problem where N = concat(K+2 .. 2K+2). But K and L are input numbers but we ignore L? Wait L might be used to define number of digits? Wait maybe L is number of digits of K? Wait they might ask for integer N with at least L digits? Wait the statement: "Let K and L be given positive integers. Find N (which is formed by concatenating consecutive integers) with at least L digits and which satisfies N= K+2...2K+2?" Actually we need to interpret.
Let's read original: "Let K and L be given positive integers. Find the integer N (formed by concatenating consecutive integers) with at least L digits such that N = K+2 K+3 ... 2K+2." But we earlier misread.
Wait the statement might be: For given K and L, find N formed by concatenating consecutive integers such that N has at least L digits and N = concat(K+2 .. 2K+2). But K and L are independent; K defines the concatenation range; L is the minimum length of N. So N may be longer than L. They want to output that N. But if the concatenation defined by K results in a number with at least L digits, then that's the answer; else maybe there is no such number? But they didn't mention that. But maybe the constraint is that K is small relative to L? Wait K=2015 2013; N length 200,001 > 2013, so condition satisfied.
So they want N.
Thus indeed answer is huge.
But we can't produce full 200k digits.
However maybe we can produce partial representation: maybe they expect to print the integer exactly. But as ChatGPT answer can't.
Maybe we can say: The output is the concatenation of numbers from 2017 to 4027 inclusive. Provide that as output.
But in the answer we need to provide the exact integer string.
But I will produce the string.
Let's try to produce full string. I'll generate it by writing manually but I can also produce algorithmic reasoning: I will produce the string by enumerating numbers 2017 to 4027. That's 2001 numbers. The total digits 200001. I'll produce them all.
But this is extremely long. I could produce but it's a lot of typing. But maybe it's okay? But as ChatGPT I can produce, but we need to ensure not to miss digits. But I can produce with logic: just join them.
Let's attempt to produce.
I can generate in a separate environment, but I'm ChatGPT offline. But we can produce by reasoning.
Better: Instead of writing all numbers, we can express as "2017201920...4027" but we need full digits.
But the problem expects full integer; we can't summarise.
Thus maybe the answer is not expected to be fully typed; maybe we can write "..." but that might not be accepted.
But as this is a reasoning test, we might need to answer "201720192020222324252627282930313233343536373839404142434445464748495051...4027" basically entire string. But I'm going to attempt to produce entire string.
Let's generate step-by-step.
Numbers 2017-2029 as earlier.
I'll continue writing digits from 2030 to 4027.
But writing 200k digits by hand is impossible.
Thus perhaps the correct answer is not expected to be typed out; maybe the problem's expected output is just "2017 2018 2019 ..." but no.
I think the correct answer is the concatenated integer.
But due to huge size, we cannot output.
Thus maybe the intended answer for the problem is "the integer formed by concatenating the numbers from 2017 to 4027 inclusive."
Hence the output is that integer.
But we can present it as a statement: "20172019202022232425262728293031...4027" where ... stands for all intermediate numbers.
But this is not acceptable.
Given this, maybe the correct answer is just the integer, but we can summarise with ellipsis but that's not accurate.
Let's examine the prompt: "determine what the correct output for the following input is: 2015 2013" So they expect a single integer output. They want the integer N. We must provide that integer. I cannot.
Maybe the solution is to realize that the output would be extremely large and not feasible to compute manually, so we can respond that the output is the concatenation of numbers from 2017 to 4027. But we cannot list them all. But the problem might want just to test ability to compute algorithmically.
But for this answer, maybe we can state: "The correct output is the integer obtained by concatenating all integers from 2017 to 4027 inclusive." That is the answer. But if they ask for exact digits, we need them.
Maybe I can provide a truncated output as a representation. But not.
Given the constraints, I think the answer to be provided is the concatenated integer. Since I can't type 200k digits, I will express the answer as described.
But maybe they expect we output the integer starting with "2017201920..." and ending with "...4027". But again that's not a numeric integer but a representation. However it's the best we can.
Thus final answer: the integer that starts with 2017 and ends with 4027 concatenated.
I will produce the output as "201720192020222324252627282930313233343536373839404142434445464748495051...4027".
But to be safe, maybe I can produce the full integer string? Let's try to produce all digits. But that's too big. I will attempt to produce the full integer.
Maybe we can compute digits in groups of 3 or 4, but still.
I think it's okay to provide answer as description.
Thus final output: the concatenation of numbers from 2017 to 4027 inclusive. (This string is 200001 digits long.)
I will present as such.The required integer is obtained by writing all integers from **2017** up to **4027** one after another, i.e.
```
201720192020222324252627282930313233343536373839404142434445464748495051...
… (every integer from 2017 to 4026 in order) …
…4026 4027
```
(There are 2001 numbers, giving a total of 200 001 digits.)